Yeah that was a total typo on my part. You can even see in the formula I typed there was no integral, I don't know why I put it there. My tired-ness is catching up with me. But apart from that integral typo, it seems to be correct according to Plato's link.

And Plato, I typed in the second problem into that website and it said:

Yeah that was a total typo on my part. You can even see in the formula I typed there was no integral, I don't know why I put it there. My tired-ness is catching up with me. But apart from that integral typo, it seems to be correct according to Plato's link.

And Plato, I typed in the second problem into that website and it said:

This is what I typed into the search box:

derivative of (x^3+1) ^tan x

You can just input the equation directly and wolfram will pull up the integral, limit, derivative, etc of the function without you having to say a word!

Also, you could do this,

Let

Now we can implicitly differentiate the left side and apply the product rule to the right side. Should clear everything up.